For the Brown Butter Pie Crust:

1. Brown the Butter:

   • In a medium saucepan, melt the 1 cup of butter over medium heat. Continue to cook, swirling the pan occasionally, until the butter turns golden brown and has a nutty aroma (about 5-7 minutes). Be careful not to burn it. Remove from heat and set aside to cool to room temperature.

2. Make the Pie Crust:

   • In a large bowl, whisk together the 2 ⅔ cups of flour and ¾ teaspoon of sea salt. Add the cooled brown butter and mix until the mixture resembles coarse crumbs.
   • Gradually add the ½ cup water and 1 tbsp vinegar, stirring until the dough comes together. If the dough is too dry, add more water, a tablespoon at a time.
   • Divide the dough into two portions, flatten into discs, wrap in plastic wrap, and refrigerate for at least 30 minutes to chill before rolling out.

For the Strawberry and Peach Filling:

3. Prepare the Filling:
   • In a large bowl, combine the sliced peaches and quarter strawberries. Add the ¼ cup granulated sugar, ¼ cup + 1 tbsp cornstarch, 1 tbsp lemon juice, 1 tsp lemon zest, and ¼ tsp sea salt. Toss everything together to coat the fruit evenly.

Assembling the Pie:

4. Roll Out the Dough:

   • On a lightly floured surface, roll out one of the dough discs to fit your pie dish (about 9 inches in diameter). Place the dough into the pie dish, trimming any excess dough hanging over the edges.
   • Pour the prepared strawberry and peach filling into the crust, spreading it out evenly.

5. Top the Pie:

   • Roll out the second dough disc and place it over the filling. You can either cover the entire pie or cut the dough into strips to create a lattice crust. If using a full crust, make sure to cut slits in the top for steam to escape.
   • Brush the top crust with the whisked egg to give it a golden, shiny finish.

6. Bake:

   • Preheat the oven to 375°F (190°C). Place the pie on a baking sheet (to catch any drips) and bake for 45-50 minutes, or until the crust is golden and the filling is bubbling.
   • If the crust starts to brown too quickly, cover the edges with aluminum foil to prevent burning.

7. Optional Sugar Topping:

   • Before baking, sprinkle the Turbinado sugar over the top crust for a little extra sweetness and crunch.

8. Cool and Serve:

   • Allow the pie to cool for at least 1 hour before serving to let the filling set. Serve warm or at room temperature with a scoop of vanilla ice cream or whipped cream for extra indulgence.